This sections describes the class orientation and gives an overview how to work with crystal orientation in MTEX.

Class Description

In texture analysis crystal orientations are used to describe the alignment of the crystals within the specimen. A crystal
orientation is defined as the rotation that maps the specimen coordinate system onto the crystal coordinate system. Since
the crystal coordinate system and the specimen coordinate system are well defined only up to crystal symmetry and specimen
symmetry, an orientation is in general represented by a class of crystallographically equivalent rotations. In MTEX the class
orientation is an inheritance of the class rotation. In particular, every function that is defined for a rotation is also available for an orientation.

Defining a Crystal Orientation

In order to define a crystal orientation one has to define crystal and specimen symmetry first.

Calculating Misorientations

Let cs and ss be crystal and specimen symmetry and o1 and o2 two crystal orientations. Then one can ask for the misorientation
between both orientations. This misorientation can be calculated by the function angle.

angle(rot * o1,o1) / degree

ans =
30.0000

This misorientation angle is, in general, smaller than the misorientation without crystal symmetry which can be computed via

angle(rotation(o),rotation(o1)) /degree

ans =
60.0000

Calculating with Orientations and Rotations

Besides the standard linear algebra operations there are also the following functions available in MTEX. Then rotational angle
and the axis of rotation can be computed via then commands angle(o) and axis(o)

Plotting Orientations

The plot function allows you to visualize an orientation in axis angle space in relation to its fundamental region.

oR = fundamentalRegion(o1.CS,o1.SS)
plot(oR)
hold on% plot the orientation as it is
plot(o1,'markercolor','b','markerSize',10)
% plot the orientation within the fundamental zone
plot(o1.project2FundamentalRegion,'markercolor','r','markerSize',10)
hold off